Tuning orbital-selective phase transitions in a two-dimensional Hund’s correlated system

Hund’s rule coupling (J) has attracted much attention recently for its role in the description of the novel quantum phases of multi-orbital materials. Depending on the orbital occupancy, J can lead to various intriguing phases. However, experimental confirmation of the orbital occupancy dependency has been difficult as controlling the orbital degrees of freedom normally accompanies chemical inhomogeneities. Here, we demonstrate a method to investigate the role of orbital occupancy in J related phenomena without inducing inhomogeneities. By growing SrRuO3 monolayers on various substrates with symmetry-preserving interlayers, we gradually tune the crystal field splitting and thus the orbital degeneracy of the Ru t2g orbitals. It effectively varies the orbital occupancies of two-dimensional (2D) ruthenates. Via in-situ angle-resolved photoemission spectroscopy, we observe a progressive metal-insulator transition (MIT). It is found that the MIT occurs with orbital differentiation: concurrent opening of a band insulating gap in the dxy band and a Mott gap in the dxz/yz bands. Our study provides an effective experimental method for investigation of orbital-selective phenomena in multi-orbital materials.


REVIEWER COMMENTS
Reviewer #1 (Remarks to the Author): The Manuscript by Ko et al discusses the manipulation of orbital occupation in a ruthenate using epitaxial strain. The authors controlled the relative occupancy of the three t2g orbitals by controlling epitaxial strain. They show using a combination of photo-emission and optical experiments that a monolayer ruthenate film undergoes a MIT as the strain is modulated from being compressive to tensile. In general, the work is well done and I think that this will be a good addition to the literature on orbital-selective phase transitions. However, I suggest that the following be addressed before publication: i) The correlation between strain and spectral changes are based on theoretical strain values. I did not see any structural data that measures the actual strain in the SRO monolayers. Given that there is an SRO layer and an STO layer on substrate -the assumption of coherent strain transmission needs to be supported.
ii) The role of surface changes and influence of surface states was not discussed at all -for a 1 ML film, accounting for contributions from the surface may be necessary. At the least a discussion on possible contributions from the surface and how that would influence the conclusions of this work would be useful.
iii) the films were annealed at 570C for 20 mins in the ARPES chamber before measurementsoxygen vacancy creation is a possibility under these conditions. How did the authors rule out contributions from oxygen vacancies? evolution of the spectral weight with strain, they interpreted the results as coming from the relative shift in energy of dxy and dxz/dyz orbitals induced by tetragonal distortions and electronic correlations.
The authors used data from ARPES to determine the orbital character of states below the Fermi energy. They checked that orbitals closer to EF are dxy, while those down in energy are of dxz/dyz character.
I think that this is an interesting work that combines efforts of materials science with fundamental insights into the physics of correlated systems. I have a couple of comments: First, I suggest making a bit clearer the discussion about the orbital hierarchy inferred from ARPES. The experiments show that under positive strain, where c/a < 1, the dxz/yz orbitals are further away from EF than dxy orbitals. This is not compatible with an orbital hierarchy fully determined from c/a tetragonality, since for c/a < 1 one should expect dxy states to be lower in energy (as depicted in Fig.  1b). This observation could be used by the authors to reinforce their viewpoint. A Mott transition with UHB/LHB splitting in the dxy/dxz sector would be compatible with ARPES observations, which otherwise could not explain by pure distortion effects. On the other, I suggest the authors to discuss the c/a parameter as extracted from STEM and include this discussion in the manuscript.
My second comment is about the role of spin-orbit coupling (SOC), which is relevant in 4d ions (SOC is in the range of 0.2-0.3 eV for these ions) but is not discussed at all in the manuscript. The physics of SOC in t2g systems is described in some references (see, e.g., Streltsov et al., Phys. Rev X 10, 031043 (2020) or Khomskii andStreltsov, Chem. Rev. 121, 5, 2992 (2021)). The \Delta_t "crystal field" parameter, originated by the c/a distortion, is in the range of a few hundreds of meV (as inferred from EDCs data in Fig. S5). This is not far from energy scales of SOC in 4d or from exchange coupling energy. In particular, my question is whether the LHB band (inferred from ARPES experiments, see Figures 5 or S5) is split because of SOC. Maybe the energy resolution is not enough to discriminate the splitting, but in any case, I suggest the authors to discuss the role of spin-orbit coupling in the physics of the orbital-selective phase transitions discussed in this manuscript.
Reviewer #3 (Remarks to the Author): The authors design and realize a smart way to tune the band structure of SrRuO3 by growing thin films on top of different substrates avoiding distortions in the oxygen octahedra. This allows them to detect a metal insulator transition as a function of the strain induced by the substrate. The authors adscribe the transition to an orbital selective Mott transition due to Hund's physics. I have some concerns with several of their arguments and discussion: -The phase diagram in Fig. 1ª is confusing, and it seems to me partially wrong. As far as I understand the J/4 and J=0 have to be compared with the negative crystal field splitting in Ref. 14 (figs. 1a and 3a). There are however several differences: (i) Why is the crystal field here given in eV? Ref.14 seems to be given in units of the half-bandwidth D. (ii) The J=0 boundaries do not show the same tendencies as in Fig.3a of Ref.14. (iii) Moreover plotting the J=U/4 and J=0 is confusing especially because they color the phase diagram following the J/4 lines. I suggest the authors plot the two values of Hund's coupling separately and be careful when plotting the lines.
-I think that the experimental MIT is robust. As far as I understand the authors claim that this MIT corresponds to the transition between a metal with both dxy and dzx/dyz orbitals partially filled and an insulator with dxy fully occupied and dzx/dyz half-filled. They argue that this is a proof of Hund's physics. While Hund's coupling increases the range of U/W in which this transition can happen, as observed in Fig.3a of Ref.14 this transition can also happen at J=0. Therefore in my opinion the authors cannot claim that they observe Hund's physics.
-I think that the numbers of the interactions do not match well the arguments from the authors. If I understand the arguments by the authors, from Fig.3 they obtainU-J~1.2 eV, U+J~2.4 eV, thus J~0.6 eV and U~1.8 eV. But in Fig.5 the lowerHubbard band is centered around -1.6eV. This value can be expected to be aroundU/2. Then I would expect U to be around 3.6 eV, much larger than the value obtained in Fig.3. Am I wrong with the interpretation of the results? Could the authors comment on this?-Can the authors give more detailed information about the effective tightbinding that they obtain from the Wannierization for the t2g orbitals?. In particular how much does it change the crystal field with the strain? Is there any change in the bandwidth of the non interacting band? And particularly for the dzx and dyz subspace? Also, which value of U do the authors use in the calculations? How large is the orbital dependent bandwidth? I think that I have not seen any of this information either in the main text or in the supplemental material.
-Can the authors give in Fig. 3h the DMFT electron filling for the cases with strain 1.7 and 2.5%. This is relevant for the interpretation of the ARPES results.
Due to all these concerns, in my opinion the manuscript, at least in its present version is not suitable for publication in Nature Comm.

Dear Reviewers
We greatly appreciate insightful and helpful comments from all the reviewers. Based on the suggestions, we performed additional experiments as well as theoretical calculation. The new results were added as supplementary figures. Also, we have gone through sincere efforts to revise the manuscript to prevent grammatical errors, making the manuscript more readable and explicit. We believe that, thanks to the comments, our manuscript is much improved and ready for resubmission.
Please find below our responses to the reviewers' comments. In Part A, we have our point-bypoint responses to the reviewers' comments. In Part B, a list of changes in the revised manuscript and supplementary information are provided.

Reviewer #1
The Manuscript by Ko et al discusses the manipulation of orbital occupation in a ruthenate using epitaxial strain. The authors controlled the relative occupancy of the three t2g orbitals by controlling epitaxial strain. They show using a combination of photo-emission and optical experiments that a monolayer ruthenate film undergoes a MIT as the strain is modulated from being compressive to tensile. In general, the work is well done and I think that this will be a good addition to the literature on orbital-selective phase transitions. However, I suggest that the following be addressed before publication: We thank the reviewer for the careful review of our manuscript and also for acknowledging the importance of our work. We have answered all questions from the reviewer as shown below.
1. The correlation between strain and spectral changes are based on theoretical strain values. I did not see any structural data that measures the actual strain in the SRO monolayers. Given that there is an SRO layer and an STO layer on substrate -the assumption of coherent strain transmission needs to be supported.
In the original manuscript, we assumed, without providing experimental structural information, that both SrRuO3 (SRO) and SrTiO3 (STO) layers on substrates were fully strained. We agree that providing structural data regarding the coherent strain is essential. To measure the in-plane lattice constants of films, we performed reciprocal space mapping (RSM) experiments with Xray diffraction (XRD). We also obtained the lattice constants from scanning transmission electron microscope (STEM) data. We measured the (103) diffraction peak of the substrate and STO layers. Identical qx values for the substrate and STO layer indicate that the films are fully strained to the substrate for both compressive and tensile strains. While SRO layers were too thin to observe diffraction peaks, it is reasonable to assume that SRO layers are also fully strained to the substrate as both the STO buffer and capping layers are fully strained to the substrate. Furthermore, we estimated the lattice constants from STEM results measured in the high-angle annular dark field (HAADF) mode. Figure A2 shows the lattice constants for the films on LSAT(001) and SAGT(001) substrates. They give -1.4% and + 0.2% strain compared to the bulk SRO lattice constant, respectively. We  We made the following changes to the revised manuscript. (Added, in the 9 th paragraph) The analysis of lattice constants from the STEM results shows coherent strain state (Supplementary Fig. 4). To investigate the thickness inhomogeneity of our SRO monolayers, we performed both macroscopic (atomic force microscopy (AFM) measurements and reflection high-energy electron diffraction (RHEED)) and microscopic measurements (STEM). Figure A3 is an AFM image of SRO(1 u.c.)/STO(10 u.c.) on STO(001) substrate, which shows step terraces. Figure A4 shows RHEED patterns of substrates and SRO monolayers. Considering our experimental geometry (electron-beam energy of ~15 keV and incidence angle of ~ 3° from the surface), the probing depth should be around 0.4 nm, which is the thickness of one layer of SRO [D. Tang et al., Physical Review B 50, 24 (1994)]. RHEED results of SRO monolayers on various substrates always show 2D-like patterns, indicating that the surface of SRO monolayers has very small roughness (i.e. small thickness inhomogeneity). STEM results also show that a film is mostly 1 u.c. thick. However, some regions in STEM results show thickness inhomogeneities (i.e., 0 or 2 u.c. of SRO) ( Figure A5, Supplementary Fig. 3). Such inhomogeneities can significantly affect some experimental measurements such as transport properties. On the other hand, area-averaged signal is obtained in ARPES experiments. As our films are mostly 1 u.c. thick, we believe the average spectroscopic response should represent that of an SRO monolayer.   Finally, to minimize surface chemical adsorbates, we post-annealed as-grown SRO samples without exposing them to the air before ARPES measurements. Such process allows us to have a high quasi-particle peak to high-binding peak intensity ratio (IQP/IHB) as reported in B. Sohn et al., Nature Communications 12, 6171 (2021). Moreover, we performed LEED experiments before/after the post-annealing process, with the results shown in Figure A6. We can see a clear enhancement in sharpness of LEED peak after the post-annealing. From this, it was confirmed that annealing was helpful in improving the surface quality of samples. We made the following changes to the revised manuscript.  (Supplementary Fig. 11).
3. The films were annealed at 570 C for 20 mins in the ARPES chamber before measurementsoxygen vacancy creation is a possibility under these conditions. How did the authors rule out contributions from oxygen vacancies?
The reviewer raised a valid concern. This can be an issue if the annealing is not properly done.
For such reason, the annealing condition has been carefully studied and we used the established annealing condition for all the samples before ARPES measurements. Therefore, the possible oxygen vacancy formations in SRO should not be an issue for the observed metal-insulator transition. Here are more details on the annealing condition.
For ARPES measurements of ultrathin films, we followed the annealing method reported in B.
Sohn et al., Nature Communications 12, 6171 (2021). The films were annealed before ARPES measurements to obtain clean surfaces. In order to find the optimal annealing condition, temperature-dependent post-annealing was performed and photoemission spectra were taken. It was found that the optimized post-annealing condition was around 600 °C. Degradation of SRO after annealing over 600 °C was reported in same study. Therefore, we post-annealed SRO at 570 °C to avoid damage from accidental temperature fluctuation. The quasi-particle peak intensity to the high-binding peak intensity ratio (IQP/IHB) was the largest under the condition   The reviewer is right. We revised the sentence as follows: (Original in the 3 rd paragraph) For instance, the three t2g orbitals split into dxy and dxz/yz levels if the oxygen octahedron is elongated along the in-plane directions (c < a).
We revised the sentence as follows: (Original in the 7 th paragraph) We used strain engineering to elongate the oxygen octahedra in SRO monolayers.
(Revised) We used strain engineering to compress the oxygen octahedra along the out-of-plane direction in SRO monolayers.
3) Line 137-139, Isn't the statement: "the transition from dxz to dxy (or dyz) not allowed" only true in the absence of any p-d hybridization?
The reviewer is right that the d-d transition is not allowed only when p-d hybridization is absent.
This was meant to state that the transition is small. The strength of p-d hybridization can be estimated based on the orbital geometry. For example, there can be strong hybridization between px/y of equatorial oxygen ion -dxy of ruthenium ion while the hybridization between pz -dxy is small due to the orbital geometry. In the case of dxz orbitals, they have a strong hybridization with pz orbital of equatorial oxygen ion, and with px orbital of apical oxygen ion, but a small hybridization with px/y orbital of equatorial oxygen ion. Therefore, the transition from dxy to dxz always involves a small hybridization and thus should be small due to the small orbital overlap.
We revised the sentence as follows: (Original in the 10 th paragraph) Specifically, the transition from dxz to dxy (or dyz) not allowed, given that there is only a small overlap between the corresponding orbitals.
(Revised) Specifically, the transition from dxz to dxy (or dyz) will be small, given that there is only a small overlap between the corresponding orbitals. 4) Lines 177-179: "The MIT occurs at a strain of approximately +0.2%" I think that the data does not support this statement. The MIT could be anywhere between -0.5% and +0.2%.
We agree with the reviewer that the MIT could occur between -0.5% and +0.2%. We revised our claim accordingly.
(Original in the 14 th paragraph ) These strain-dependent DOSs at EF in the SRO monolayer indicate that MIT occurs at a strain of approximately +0.2%, which agrees well with the optical spectra of the SRO monolayer (Fig. 3g, h).
(Revised) These strain-dependent DOSs at EF in the SRO monolayer indicate that MIT occurs at a strain between -0.5% and +0.2%, which agrees well with the optical spectra of the SRO monolayer (Fig. 3g, h).

Reviewer #2
The authors of this manuscript report on a metal insulator transition driven by orbital selective occupancy of orbitals in strained monolayer SrRuO3 films. The transition is controlled by the degree of tetragonal distortion of the unit cell imposed by growing the monolayers on top of a variety of substrates that span a range between compressive to tensile stress. Based on ellipsometric and ARPES experiments, the authors infer a Mott transition taking place in the dxz/dyz subset as the tensile strain grows sufficiently. The latter is ruled by strong correlations dictated by the ratio between Hund's coupling J and the U correlation energy.
To obtain reliable results, the authors devise a way to control the field splitting due to the tetragonal distortion, by developing a symmetry-preserving strain engineering technique (i.e., by inserting a STO layer between substrate and SrRuO3 monolayer). The success of this strategy was confirmed by LEED diffraction patterns and transmission electron microscopy. This guaranteed that the relevant parameter was the c/a distortion and make reliable the comparison between the samples with different strain state. They subsequently used ellipsometry over a wide range of frequencies and identified three main peaks. The authors propose specific transitions between electronic states in the t2g manifold, ruled by parameters U and J. They assumed that electrons are transferred to neighboring sites in the lattice by interacting with light, which I think is a reasonable and justified hypothesis. Based on the evolution of the spectral weight with strain, they interpreted the results as coming from the relative shift in energy of dxy and dxz/dyz orbitals induced by tetragonal distortions and electronic correlations.
The authors used data from ARPES to determine the orbital character of states below the Fermi energy. They checked that orbitals closer to EF are dxy, while those down in energy are of dxz/dyz character. I think that this is an interesting work that combines efforts of materials science with fundamental insights into the physics of correlated systems. I have a couple of comments: We thank the reviewer for the comments. We have answered both of the questions as follows.
1. First, I suggest making a bit clearer the discussion about the orbital hierarchy inferred from ARPES. The experiments show that under positive strain, where c/a < 1, the dxz/yz orbitals are further away from EF than dxy orbitals. This is not compatible with an orbital hierarchy fully determined from c/a tetragonality, since for c/a < 1 one should expect dxy states to be lower in energy (as depicted in Fig. 1b). This observation could be used by the authors to reinforce their viewpoint. A Mott transition with UHB/LHB splitting in the dxy/dxz sector would be compatible with ARPES observations, which otherwise could not explain by pure distortion effects. On the other, I suggest the authors to discuss the c/a parameter as extracted from STEM and include this discussion in the manuscript.
We thank the reviewer for helping us make the discussion clearer. As the reviewer mentioned, the c/a < 1 makes the dxy orbital level lower than the dxz/yz level when only the tetragonal distortion effect is considered. Therefore, dxy is fully filled while dxz/yz is half-filled when U = J = 0 (as illustrated in the middle figure of Figure B1). In real SRO (with sizable U and J), the halffilled dxz/yz will open a Mott gap (as shown in the right figure in Figure B1). This makes dxz/yz orbitals farther away from EF than the dxy orbital. In other words, in addition to the pure structural distortion, effects of U and J should be considered to elaborate on the observed electronic structures in SRO as the reviewer correctly pointed out. and Hund's rule coupling (J). (Figure 1b) To make it clearer, we made the following changes.  whereas that of SRO monolayer on SAGT(001) is 101.8%, confirming that tensile strain leads to a smaller c/a value.
Although the trend that tensile strain reduces the c/asub value is consistent with the expectation, the value from the STEM analysis is not exactly same as the expected value. A potential source for the difference is that the STO capping layer (for the protection of the SRO layer during STEM measurements) could affect the structure of the underneath SRO layer. In addition, assigning precise position at the interfaces can be challenging due to cation mixing or step terraces, leading to large error bars. Therefore, only the qualitative aspect of the result should be taken.  (2021)). The ∆t "crystal field" parameter, originated by the c/a distortion, is in the range of a few hundreds of meV (as inferred from EDCs data in Fig. S5). This is not far from energy scales of SOC in 4d or from exchange coupling energy. In particular, my question is whether the LHB band (inferred from ARPES experiments, see Figures 5 or S5) is split because of SOC.
Maybe the energy resolution is not enough to discriminate the splitting, but in any case, I suggest the authors to discuss the role of spin-orbit coupling in the physics of the orbital-selective phase transitions discussed in this manuscript.
We thank the reviewer for the suggestion. As for the band splitting in the LHB the reviewer mentioned, it may not be experimentally observed because of the breadth of the incoherent LHB at the high binding energy.
We have the following sentence in the revised manuscript to address the issue.
(Added in the 12 th paragraph) Note that existence of such orbital polarization alludes to an insignificant role of the spin-orbit coupling in the orbital dependent Mott transition in the ruthenate films 39 .

Reviewer #3
The authors design and realize a smart way to tune the band structure of SrRuO3 by growing thin films on top of different substrates avoiding distortions in the oxygen octahedra. This allows them to detect a metal insulator transition as a function of the strain induced by the substrate. The authors ascribe the transition to an orbital selective Mott transition due to Hund's physics. I have some concerns with several of their arguments and discussion: We thank the reviewer for acknowledging the novelty of our work and also for the helpful comments. We responded to all the questions raised and revised the manuscript accordingly. Fig. 1a is confusing, and it seems to me partially wrong. As far as I understand the J/4 and J = 0 have to be compared with the negative crystal field splitting in Ref.

The phase diagram in
14 (figs. 1a and 3a). There are however several differences: (i) Why is the crystal field here We thank the reviewer for the very helpful comment. The phase diagram in Figure 1 in the original manuscript can be confusing and mislead the readers. Therefore, we revised Figure 1c as the reviewer suggested (see Figure C1).    (Figure 1c) 2. I think that the experimental MIT is robust. As far as I understand the authors claim that this MIT corresponds to the transition between a metal with both dxy and dzx/dyz orbitals partially filled and an insulator with dxy fully occupied and dzx/dyz half-filled. They argue that this is a proof of Hund's physics. While Hund's coupling increases the range of U/W in which this transition can happen, as observed in Fig.3a of Ref.14 this transition can also happen at J = 0. Therefore in my opinion the authors cannot claim that they observe Hund's physics.
We agree that the observation of the orbital-selective phase transition itself is not a direct evidence for the Hund's physics. A direct observation of Hund's physics is challenging because tuning J value is experimentally difficult. In this study, we suggest an indirect way to control the orbital occupancy for the study of phase transition in Hund's system. We wanted to address that the phase transition in 2D SRO can provide insight on the Hund's physics. We revised the sentences that can mislead the readers (please see below).
We made the following revisions: (Original in the 2 nd paragraph) The J value is usually determined by atomic physics, so control of its value is difficult without chemical substitution. To control orbital occupancy, earlier studies used doping and/or substitution with different chemical elements.
(Revised) Direct control of the J value is experimentally difficult as it is usually determined by atomic physics. On the other hand, an alternative but indirect approach to control orbital occupancy is possible via doping and/or substitution with different chemical elements.
(Original in the 4 th paragraph) In this study, we investigated how Hund-driven phase transitions can occur in SrRuO3 (SRO) films by artificially controlling the crystal field splitting.
(Revised) In this study, we investigated tuning of orbital occupancy in SrRuO3 (SRO) ultrathin films by artificially controlling the crystal field splitting. It should be noted that Sr2RuO4 is wellknown as Hund's metal, so 2D limit of SRO can provide insight on the Hund's physics 7 (Original in the 2 nd paragraph) Therefore, precise control of orbital occupancy without random chemical distribution is the key for experimentally investigating Hund-driven phase transitions.
(Revised) Therefore, precise control of orbital occupancy without random chemical distribution is the key for experimental investigation of phase transitions in Hund's systems.
What we would like to address was that the observed strain induced MIT shows a character of bandwidth change affects the electronic structure of SRO, we measured temperature-dependent ARPES of SRO with +0.2 % of strain which is insulating at low temperature. As shown in Figure C2, the data exhibit a robust insulating phase between 6 and 160 K with the lower Hubbard band (LHB) of dxz/yz character. In other words, the Mott transition in this system cannot be induced by band-width change in tensile-strained film. Therefore, we believe the robust strain-induced Mott gap opening is an indication of a Hund's system (again, not an evidence as the reviewer pointer out). 3. I think that the numbers of the interactions do not match well the arguments from the authors.
If I understand the arguments by the authors, from Fig.3 they obtain U -J ~ 1.2 eV, U + J ~ 2.4 eV, thus J ~ 0.6 eV and U ~ 1.8 eV. But in Fig.5 the lower Hubbard band is centered around -1.6 eV. This value can be expected to be around U/2. Then I would expect U to be around 3.6 eV, much larger than the value obtained in Fig.3. Am I wrong with the interpretation of the results?
Could the authors comment on this?
We thank the reviewer for bringing up the comparison between energy scales of electronic correlations and ARPES band peak positions. Second, as the reviewer pointed out, the energy position of the LHB measured by ARPES is about 1.6 eV below EF. In the case of a single-band system, this band will split symmetrically by (U+J)/2 around EF. However, in multi-orbital systems, the presence of other band makes the energy levels of LHB and UHB asymmetric around EF. In the case of monolayer SRO, EF will be located between the dxy band (not LHB) and UHB, which are the top of valence band and the bottom of conduction band, respectively. In an analogous system of Ca2RuO4 which has the same orbital hierarchy and Mott insulating behavior, DMFT results show that UHB is closer to 4. Can the authors give more detailed information about the effective tight-binding that they obtain from the Wannierization for the t2g orbitals? In particular how much does it change the crystal field with the strain? Is there any change in the bandwidth of the non interacting band?
And particularly for the dzx and dyz subspace? Also, which value of U do the authors use in the calculations? How large is the orbital dependent bandwidth? I think that I have not seen any of this information either in the main text or in the supplemental material.
We thank the reviewer for raising the point. We left out detailed but important information on the theory part in the original manuscript. Figure C4 shows detailed band structures obtained from the Wannierization for the t2g orbitals. In addition, strain dependent crystal field splitting (∆t = Exz/yz -Exy) is shown in Figure C5. Electron hopping terms for dxy-dxy and dxz-dxz (or dyz-dyz) are shown in Figure C6. In this study, we used U = 2.7 eV and J = 0.45 eV (J = U/6).   We made the following changes to the manuscript (Original, in the 12 th paragraph) Dynamic mean-field theory (DMFT) calculations with J = U/6 also revealed that the filling of dxy (dxz/dyz) orbitals increased (decreased) with an increase in strain (Fig. 3h).
(New figures) Figure C4 and Figure C6 are included in the Supplementary as Fig. 13 and Fig. 14. Fig. 3h the DMFT electron filling for the cases with strain 1.7 and 2.5%. This is relevant for the interpretation of the ARPES results.

Can the authors give in
We performed DMFT electron filling calculation with + 1.7 % and +2.5 % of strain. The results in Figure C7 shows that further tensile strain makes dxy fully filled, which is consistent with the ARPES results. We made the following changes to the manuscript.
(New figure) Figure C7 is included in the Supplementary as Fig. 6. (Original, in the 12 th paragraph) When the strain reaches +0.2%, dxy becomes fully-filled, and dxz/yz becomes half-filled (Revised) When the strain is +0.2% or higher, dxy is fully-filled while dxz/yz is half-filled ( Supplementary Fig. 6).
6. Due to all these concerns, in my opinion the manuscript, at least in its present version is not suitable for publication in Nature Comm.
We sincerely appreciate the reviewer's comments which greatly helped us improve the manuscript. Based on the reviewer's comment, we revised our manuscript. Figure 1 and introduction were revised. We performed additional experiments and calculations as well. We believe that our revised manuscript is more solid and accurate.